This proposed research is motivated by the need for novel phase I and II cancer clinical trial designs exploring safety and efficacy of drug combinations of two or more cytotoxic and biologic agents with continuous dose levels. Current research on this subject relies on a search for optimal doses among a fixed a priori set of a relatively small number of dose combinations of two agents. Moreover, most of these methods recommend a single dose combination as the phase II dose. As a result, these designs can fail to identify the true optimal toxicity and efficacy dose combinations and require larger sample sizes as the number of dose combinations and number of agents increase. These methods also lack user friendly software. Our proposal consists of three aims. In aim 1, we will develop several methods using Bayesian adaptive designs known as escalation with overdose control (EWOC) and the continual reassessment method (CRM) to estimate the maximum tolerated dose (MTD) curve or surface of two or more cytotoxic/biologic agents. We will consider cases where (i) the dose limiting toxicity (DLT) is binary, presence or absence of DLT within one cycle of therapy and (ii) DLT is time to event, also known as late onset toxicity. In Aim 2, we will develop Bayesian adaptive designs for early phase cancer clinical trials to estimate the optimal toxicity and efficacy contour of two or more cytotoxic/biologic agents. We will first develop seamless phase I/II designs for estimating the MTD curve or contours of several agents and identify the optimal dose combination(s) that maximize efficacy in a two-stage design. Such designs are relevant when treatment efficacy is assessed after few cycles of treatment. Because the population of subjects in phase I and II trials are likely to be very different, we wil further study alternative designs that simultaneously identify dose combination regions that maximize efficacy while not exceeding a pre-specified threshold of toxicity. These are also applicable when preliminary efficacy is assessed as biomarker modulation within one cycle of treatment. DLT and efficacy endpoints will be modeled as binary and time to event outcomes. In Aim 3, we will deploy R packages and web applications to implement designs proposed in Aim 1-2 and evaluate operating characteristics of prospective trials. The investigators of this proposal have extensive experience developing methodology for phase I clinical trials using the Bayesian adaptive designs EWOC and CRM. They have decades of experience collaborating with clinicians in designing and conducting dose finding trials in cancer. The investigators have also developed stand-alone user friendly software for designing single agent cancer phase I trials using EWOC and CRM and a fully integrated Web based application for the EWOC design.